The bandage was wound around the wound.
The farm was used to produce produce.
The dump was so full that it had to refuse refuse.
A bass was painted on the bass drum.
I don't object to the object.
The insurance was invalid for the invalid.
They were too close to the door to close it.
The wind was too strong to wind the sails.
The tears in my painting brought me to tears.
I was forced to subject to the subject.

I found these sentences in a magazine. I thought some of you might get a laugh from these.

We had to desert the hot desert
The dove dove off the roof
The minute seemed minute
The overhead is hanging overhead
It's his birthday, so I'll present him with a present
The recreation park was a recreation of the old west
I need to resume writing my resume
He moped as he rode his moped

Only 48 sounds and combinations of those, thers about 2000+ homophones I think, but that's just a guess. If you don't count kanji, then yes, but if you do then there's still some, but of course not nearly as many.

shizuka wrote:Do homographs exist in 日本語, or do the kanji eliminate that problem?

Japanese is FULL of homophones. More than in English, I would guess--for the reason Spaztick said. Try looking up "ki" in a dictionary and see how many words there are. >_< (My elec. dic. has 16 options.) Or "kai" (13) or "saikou" (7). Kanji help, though, but only when reading/writing. Without kanji, you'd have to infer which word was meant by the context of the sentence--which can be pretty difficult. >_<

As kates said there are many homophones, and if written in kana they must therefore be homographs. But yeah, in the written language kanji does eliminate this somewhat (although, there are some kanji homographs, too).